Extensive properties, examples

Differentiating between Intensive and Extensive Properties EXAMPLE 1. 2 ... 

Properties are also classified according to their dependence on the mass of a sample. An intensive property is a property that is independent of the mass of the sample. For example, temperature is an intensive property, because we could take a sample of any size from a uniform bath of water and measure the same temperature (Fig. A.2). An extensive property is a property that does depend on the mass ( extent ) of the sample. Volume is an extensive property 2 kg of water occupies twice the volume of 1 kg of water. 

Some intensive properties are ratios of two extensive properties. For example, the property density, d, mentioned above, is a ratio of the mass, m, of a sample divided by its volume, V ... 

Heat capacity is an extensive property the larger the sample, the more heat is required to raise its temperature by a given amount and so the greater is its heat capacity (Fig. 6.10). It is therefore common to report either the specific heat capacity (often called just specific heat ), Cs, which is the heat capacity divided by the mass of the sample (Cs = dm), or the molar heat capacity, Cm, the heat capacity divided by the amount (in moles) of the sample (Cm = C/n). For example, the specific heat capacity of liquid water at room temperature is 4.18 J-(°C) -g, or 4.18 J-K 1-g and its molar heat capacity is 75 J-K -mol1. 

Unlike mass and volume, density does not vary with the amount of a substance. Notice in Figure 1-20 that all the corks float, regardless of their sizes. Notice also that all the pieces of lead sink, regardless of their sizes. Dividing a sample into portions changes the mass and volume of each portion but leaves the density unchanged. A property that depends on amount is called extensive. Mass and volume are two examples of extensive properties. A property that is independent of amount is called intensive. Density and temperature are intensive properties. 

Give two examples each of intensive and extensive properties. 

This relationship is expressed in extensive properties that depend on the extent of the system, as opposed to intensive properties that describe conditions at a point in the system. For example, extensive properties are made intensive by expressing them on a per unit mass basis, e.g. s = S/m density, p 1 /v, v V/m. For a pure system (one species), Equation (1.2) in intensive form allows a definition of thermodynamic temperature and pressure in terms of the intensive properties as... 

Any property that depends on the concentration or amount of substance present. Examples of extensive properties include mass and internal energy. 

Properties that do not vary with the amount of mass of a substance - for example, temperature, pressure, surface tension, mole fraction - are termed intensive properties. On the other hand, those properties that vary in proportion to the total mass of substances - for example, total volume, total mass, and heat capacity - are termed extensive properties. 

It should be noted, however, that some extensive properties become intensive properties, in case their specific values - that is, their values for unit mass or unit volume - are considered. For example, specific heat (i.e., heat capacity per unit mass) and density (i.e., mass per unit volume) are intensive properties. 

It should be emphasized that the criterion for macroscopic character is based on independent properties only. (The importance of properly enumerating the number of independent intensive properties will become apparent in the discussion of the Gibbs phase rule, Section 5.1). For example, from two independent extensive variables such as mass m and volume V, one can obviously form the ratio m/V (density p), which is neither extensive nor intensive, nor independent of m and V. (That density cannot fulfill the uniform value throughout criterion for intensive character will be apparent from consideration of any 2-phase system, where p certainly varies from one phase region to another.) Of course, for many thermodynamic purposes, we are free to choose a different set of independent properties (perhaps including, for example, p or other ratio-type properties), rather than the base set of intensive and extensive properties that are used to assess macroscopic character. But considerable conceptual and formal simplifications result from choosing properties of pure intensive (R() or extensive QQ character as independent arguments of thermodynamic state functions, and it is important to realize that this pure choice is always possible if (and only if) the system is macroscopic. 

The thermodynamic state is therefore considered equivalent to specification of the complete set of independent intensive properties 7 1 R2, Rn. The fact that state can be specified without reference to extensive properties is a direct consequence of the macroscopic character of the thermodynamic system, for once this character is established, we can safely assume that system size does not matter except as a trivial overall scale factor. For example, it is of no thermodynamic consequence whether we choose a cup-full or a bucket-full as sample size for a thermodynamic investigation of the normal boiling-point state of water, because thermodynamic properties of the two systems are trivially related. 

The Gibbsian equilibration principles as developed previously (Chapter 5) apply straightforwardly to heterogeneous as well as homogeneous systems. Consider, for example, the heterogeneous two-phase system of phases a, /3. Extensive properties such... 

The first class comprises quantity-type ( extensive ) properties Xb such as the quantity of mass or spatial volume of the system. A distinctive characteristic of these properties is their additivity in subunits of the system, such that each is linearly proportional to overall scale (number of identical subunits), as measured, for example, by total mass. Arbitrary linear combinations of the independent Xb... 

The internal energy is an extensive property, so it depends on the amount of substance. For example, a 50-g sample of a substance has twice as much internal energy as 25 g of the same substance under the same conditions. 

The term property refers to a characteristic of a material and can be measured. Examples are pressure, temperature and volume. Properties may also be computed, such as, for example, internal energy, which cannot be measured directly. An extensive property is one whose value is the sum of each of the subsystems comprising the entire system. An example is a gas mixture, in which each constituent (or subsystem) has masses or volumes different from the original system. Thus, mass or volume is an extensive property. 

The standard free-energy change, A G°, for a reaction is the change in free energy that occurs when reactants in their standard states are converted to products in their standard states. As with AH° (Section 8.10), the value of AG° is an extensive property that refers to the number of moles indicated in the chemical equation. For example, AG° at 25°C for the reaction... 

Properties such as internal energy, volume and entropy are called extensive because their values for a given phase are proportional to the mass or volume of the phase. The value of an extensive property of an entire system is the sum of the values of each of the constituent phases. The molar value of an extensive property is that for a properly defined gram-molecular weight or mole of material. The specific value of an extensive property is that per unit weight (eg, one gram of material). A property is called intensive if its value for a given phase is independent of the mass of the phase. Temp and pressure are examples of such intensive properties... 

The thermodynamic treatment of an interface generally considers a system composed of the interface (y) and two adjacent homogeneous phases (a and / ). The extensive properties of the systems must be ascribed to these three regions, for example, the Gibbs free energy G and the number of moles of a species in the system fulfill... 

The state of a system is defined by its properties. Extensive properties are proportional to the size of the system. Examples include volume, mass, internal energy, Gibbs energy, enthalpy, and entropy. Intensive properties, on the other hand, are independent of the size of the system. Examples include density (mass/volume), concentration (mass/volume), specific volume (volume/mass), temperature, and pressure. 

A thermodynamic property is said to be extensive if the magnitude of the property is doubled when the size of the system is doubled. Examples of extensive properties are volume V and amount of substance n. A thermodynamic property is said to be intensive if the magnitude of the property does not change when the size of the system is changed. Examples of intensive properties are temperature, pressure, and the mole fractions of species. The ratio of two extensive properties is an intensive property. For example, the ratio of the volume of a one-component system to its amount is the molar volume Vm = V/n. 

Experience shows that for a system that is a homogeneous mixture of Ns substances, Ns + 2 properties have to be specified and at least one property must be extensive. For example, we can specify T, P, and amounts of each of the Ns substances or we can specify T, P, and mole fractions x, of all but one substance, plus the total amount in the system. Sometimes we are only interested in the intensive state of a system, and that can be described by specifying Ns + 1 intensive properties for a one-phase system. For example, the intensive state of a solution involving two substances can be described by specifying T, P, and the mole fraction of one of substances. 

Extensive properties of multicomponent phases (solutions) are related to the amount of material in the phase, but may not be just the sum of the properties of the constituent components. Probably the best known example of this difference is the observation that mixing 1.0 L of ethanol with 1.0 L of water at standard temperature and pressure (STP) produces 1.93 L of water-ethanol solution. We define the difference between an extensive property of the solution and the sum of the properties of its pure components as the property change of mixing for the solution ... 

Unlike free energy G, which is an extensive property (such as for example volume or internal energy), chemical potential p. is an intensive property of the system (such as e. g. temperature and pressure). For this reason the chemical potential of the solute at given temperature and pressure does not depend on the absolute amounts of individual components in the solution but solely on the relative composition, i. e. relative amounts of the substances forming the solution. 

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